ATTACHMENT A
Circular No. A-94
Revised

RRED COSTS AND BENEFITS

Assume a ten-year program which will commit the Government to
the stream of expenditures appearing in column (2) of th

table below and which will result in a series of benefits
appearing in column (3). The discount factor for a 10 percent
discount rate is presented in column (4). Present value cost
for each of the ten years is calculated by multiplying column (2)
by column (4); present value benefit for each of the ten years
is calculated by multiplying column (3) by column (4). Present
value costs and benefits are presented in columns (5) and (6),
respectively.

Present Present
Year since value value
initiation, Expected Expected Discount cost benefit
renewal or yearly yearly factor for (Coder. (2), cx: siCode. (35x
n cost benefit 10 percent Col. (4)] Gon. (4))
qT) (2) (3) (4) (3) (6)
nt $10 $0 0.909 $9.1 $0.0
2 20 0 0.826 16.5 0.90
3 30 ‘S ere 22.5 3.8
4 30 10 0.683 20.5 6.8
5 20 30 0.621 18.6
6 10 40 0.564 22.6
7 5 40 Deu 20.5
8 5 40 0.467 aE ay)
9 5 40 0.424 17.0
16 - 25 0.386 Ce!
Suet
The sum (5) is presen value
The sum (6) is present value |
Present value net benefit is ti - erence between present

value total total cost:

$117.7 = $95.5. = $22.2.

a recommended
conomy, by
Press Company,



o

a.
i)
y nadle
a eneZi ic
P Sts &: should be evaluated.

The expected annual costs and benefits (or effects) shoul
be supplemented with estimates of minimum and maximum values.
Present value cost and benefits should be calculated for
each of these estimates. The probability that each of the
possible cost and benefit estimates may be realized should
also be discussec, even when there is no basis for a precise
suancitative estimate. Uncertainty of the cost and benefit
(or effeces) estimates should be treated explicitly, as

ribec above. The prescribed discount rate should be
usec to evaluate all alternatives. Specifically, the evalua-
tions should not use different discount rates to reflect the

relative uncertainty of the alternatives.

tren

lisv. The discount rates to be
ams anc projects subject to the
as follows:
a zate of 10 percent; and, where relevant,
b. Any other rate ibec by or pursuant to law,
Executive order, or oth vant Circulars.

tibet count race of

es erage race of

se SeStilaevacL]o.
dation, Astachment B contains discount
scoun= rate of 10.0 percens for each of
hoes uety,

Det
<b

bit o
300 33

(Ne

cones =

a)
1
w
re


Year since
initiation
renewal or
expansion

DISCOUNT

Discount
factors*

Year since
initiation,
renewal or
expansion

evised

Discounts
factors?

Peete

UUM OW MINN WNEFOOMIKRUYRUNE

NNN EE ee

0.909091
0.826446
0.751315
0.683013
0.620921
0.564474
0.513158
0.466507
0.424098
0.385543
0.350494
0.318631
0.289664
0.263332
0.239392
0.217629
0.197845
0.179859
0.163508
0.148644
On35 031
0.122846
0.111676
0.101526
0.092296

26
Aes
28
29
30
ou

‘2

sis!
34
fis)
36
cha
33
39
40
cla
42
43
44
45
46
47
48

0.083505
0.076278
0.069343
0.063033
9.057309
0.052099
0.047362
0.043057
0.039143
0.035584
0.032349
0.029408
0.026735
0.024304
0.022095
0.020086
0.018250
0.016690



EXECUTIVE OFFICE OF THE PRESIDENT
OFFICE OF MANAGEMENT AND BUDGET
WASHINGTON. O.C. 20503

Marented 01 ie CIRCULAR NO. A-94
Revised

TO THE HEADS OF EXECUTIVE DEPARTMENTS AND ESTASLISHMENTS

SUBJECT: Discount rates to be used in evaluating time-
@istributed costs and benefits

l. Purpose. This Circular prescribes a standard discoun
rate to be used in evaluating the measurable costs and/or
benefits of programs or projects when they are distributec

over time.

2. Rescission. This Circular replaces and rescinds Ofzice
of Management and Budget (OMB) Circular No. A-94 dated
June 26, 1969.

Ja. 1 Scope:

a. This Circular applies to all agencies of the execu-
tive branch of the Federal Government except the U.S. Postal
Service. The discount rate prescribed in this Circular
applies to the evaluation of Government decisions concerning

ri

the initiation, renewal or expansion of all programs or .
projects, other than those specifically exemptec below, for
which the adoption is expected to commit the Government to a
series of measurable costs extending over three or more
years or which result in a series of benefits that extenc
three or more years beyond the inception date.

b. Specifically exempted from the scope of this Circular
are decisions concerning water resource projects (guidance
i is’ the approved Water Resources Principles and
, the Government of the District of Columbia, and
1 recipients of Federal loans or grants.

The remaining exemptions derive from the secondary
ef the decisions involved; that is, how to acquire

or proceed with a program after an afi ative decision
tiate, renew, or expand such a program using this

Thus:

the evalua

ae
= veal prep

OL



n

(2) This Circular would not asply to the evaluation
of decisions concerning the accuisitien of commercial-tyse
services by Government cr contractor cperation, cuidance
for whi is’ OMB Circular No. A-76,

(3) This Circular would net apply to the evaluation
of decisions concerning how to select automatic data process-
ing equirment, guidance for which is OMB Circular No. A-54
and OMB Bulletin No. 60-6.

@. The discount rates prescribed in this

(lL) Suggested for use in the

intern
documents c= the agencies in the executi

al
ve branci

(2) Required for use in program analyses submitted
to ice of Management and Budget in support of lecis-
lative and budget programs.

This Circular does net supers
prescribec by or pursuant to
relevant Circulass ies
and projec n ance wi
in additio. the present val
its using unt rate prescribed

analytic documen
Budget should be

relevant:

m : xpected annual do

vi = goocs, and sez
~ rv mam or projec.
2 based on estab-
ph Gels. am ané srojec
e bps including 3c
if ssess = be include
w or no 2 Government.
Ss SSenc = Federal saymenz
see 2a2DuS 2ues eperty anc Stac
an teis=p/<! Zorec

S. Ex>e eli: means the dollar
e a nom an ervices exzected
lel ope) a UCS ee years
Zo} ‘ a vearly benefi-
5 es and practices ¢
El Se evaluation.



cr al effects means an objective, non-
monetary rogram effects expected for each of
the years a program or project is in operation. When
dollar value cannot be placed on the effects of comparable
programs or projects, an objective measure of effects may be
available and useful to enable the comparison of alternative
means of achieving specified objectives on the basis of
their relative present value costs. These effects shouldé
be estimated for each year of the planning period and are
net to be discounted.

dad. Discount rate means the interest rate used in calcu-
lating the present value of expected yearly costs and bene-
fits)

e. Discount factor means the factor for any specific
discount rate wnich translates expected cost or benefit in
any specific future year into its present value. The discount
factor is equal to 1/(l+r)*, where r is the discount rate

and t is the number of years since the date of initiation,
renewal or expansion of a program or project.

f. Present value cost means each year's expected
yearly cost multiplied by its discount factor and then

summed over all years of the planning period.

g. Present value benefit means each year's expected
yearly benefit multiplied by its discount factor and then
summed over all years of the planning period.

the d.
nd pr

erence
and nt val

@ tn

es

-cost ratio means present value benefit
resent value cost (item £).

Ole
@ler
a
u

“e

Bu

ontains an example that illustrates calcula-
esent value information.

wy
be or

3 t inflation. All estimates of the cests and

i Goliars; i.e., in terms of the general purchasing
power c2 the dcllar at the time of decision. Estimates may _
zeflect changes in the relative prices of cost and/or benefits
comsonents, where there is a reasonable basis for estimating
such changes, but should not include any forecasted chance ©
in the general price level during the planning pericd. a

(Ne. A-94)